(0 2) (3 3) In Slope Intercept Form

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Jul 03, 2024

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Understanding (0, 2) and (3, 3) in Slope-Intercept Form

In algebra, understanding the slope-intercept form of a linear equation is crucial in graphing and analyzing linear relationships. In this article, we will explore how to write the points (0, 2) and (3, 3) in slope-intercept form.

What is Slope-Intercept Form?

The slope-intercept form of a linear equation is written in the form of y = mx + b, where:

• m represents the slope of the line (a measure of how steep it is)
• b represents the y-intercept (the point where the line crosses the y-axis)

Writing (0, 2) in Slope-Intercept Form

Given the point (0, 2), we can write it in slope-intercept form by using the following steps:

1. Since the point (0, 2) lies on the y-axis, the x-coordinate is 0.
2. The y-coordinate is 2, which means the y-intercept (b) is 2.
3. The slope (m) can be any value, since we only have one point.

Let's assume the slope (m) is 1. Then, the slope-intercept form of the equation would be:

y = 1x + 2

Simplifying the equation, we get:

y = x + 2

Writing (3, 3) in Slope-Intercept Form

Given the point (3, 3), we can write it in slope-intercept form by using the following steps:

1. The x-coordinate is 3, and the y-coordinate is 3.
2. We can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is the point (3, 3).
3. Rearranging the equation to slope-intercept form, we get:

y = m(x - 3) + 3

Since we only have one point, the value of the slope (m) can be any value. Let's assume the slope (m) is 1. Then, the slope-intercept form of the equation would be:

y = 1(x - 3) + 3

Simplifying the equation, we get:

y = x - 3 + 3

y = x

Conclusion

In conclusion, we have written the points (0, 2) and (3, 3) in slope-intercept form. Understanding how to convert points to slope-intercept form is essential in graphing and analyzing linear relationships. With practice, you'll become proficient in writing equations in slope-intercept form and unlocking the secrets of linear algebra.